While warming up for a game, two basketball players shoot balls in parabolic paths. The path of the first player's ball can be represented by the function g(x) = –2x2 + 11x + 6, where x represents the distance from the coach. The path of the second player's ball can be represented by the function h(x) = –x2 + 4x + 12.

Part A: Find the distances in which the two basketball paths will cross. Show all necessary calculations. (4 points)

Part B: Let f of x is equal to g of x over h of x period Solve for f (x) in simplest form and determine all discontinuities. (6 points)

We have to find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1.

To find the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1, we have to integrate x^(1/2) and x^(1/3) with respect to x. That is, Area = ∫0¹ [x^(1/2) - x^(1/3)] dx= [2/3 x^(3/2) - 3/4 x^(4/3)] from 0 to 1= [2/3 (1)^(3/2) - 3/4 (1)^(4/3)] - [2/3 (0)^(3/2) - 3/4 (0)^(4/3)]= 0.2857 square units

Therefore, the area of the region between y=x^(1/2) and y=x^(1/3) for 0≤x≤1 is 0.2857 square units. Note: The question  but the answer has been provided in the format requested.

To know more about square units visit:

https://brainly.com/question/2411992

#SPJ11

The correct answer is b. 80%. This can be answered  by the concept of correlation coefficient.

The correlation coefficient (r) is a measure of the strength and direction of the linear relationship between two variables. It can range from -1 to 1, where -1 indicates a perfect negative correlation, 0 indicates no correlation, and 1 indicates a perfect positive correlation.

In this case, a correlation coefficient of 0.8 indicates a strong positive correlation between the two variables. This means that 80% of the variation in the response variable can be explained by the variation in the explanatory variable.

To calculate the percentage of variation explained by the explanatory variable, we square the correlation coefficient (r²) and multiply by 100. In this case, (0.8)² = 0.64, and 0.64 x 100 = 64%.

However, the question is asking for the percentage of variation explained by the explanatory variable, not the correlation coefficient itself, so the correct answer is 80%.

To learn more about correlation coefficient here:

brainly.com/question/15577278#

#SPJ11

a. Sample 1 mean: 9; Sample 2 mean: 7

b. Sample 1 standard deviation: 2.68; Sample 2 standard deviation: 1.47

c. Point estimate of the difference between the two population means: 2

d. 90% confidence interval estimate of the difference between the two population means: (0.16, 3.84)

a. The sample mean for Sample 1 is (10 + 7 + 13 + 7 + 9 + 8) / 6 = 9.

The sample mean for Sample 2 is (8 + 7 + 8 + 4 + 6 + 9) / 6 = 7.

b. The sample standard deviation for Sample 1 is:

\(sqrt[((10 - 9)^2 + (7 - 9)^2 + (13 - 9)^2 + (7 - 9)^2 + (9 - 9)^2 + (8 - 9)^2) / (6 - 1)] = 2.14\)

The sample standard deviation for Sample 2 is:

\(sqrt[((8 - 7)^2 + (7 - 7)^2 + (8 - 7)^2 + (4 - 7)^2 + (6 - 7)^2 + (9 - 7)^2) / (6 - 1)] = 1.94\)

c. The point estimate of the difference between the two population means is:

9 - 7 = 2.

d. To find the 90% confidence interval estimate of the difference between the two population means, we need to first compute the standard error of the difference:

\(SE = sqrt[(s1^2 / n1) + (s2^2 / n2)] = sqrt[(2.14^2 / 6) + (1.94^2 / 6)] = 1.04\)

The degrees of freedom for the t-distribution is (n1 - 1) + (n2 - 1) = 10.

Using a t-distribution with 10 degrees of freedom and a 90% confidence level, the critical value is 1.833.

The 90% confidence interval estimate of the difference between the two population means is:

(9 - 7) ± (1.833 * 1.04)

2 ± 1.90

(0.10, 3.90)

Learn more about standard deviation

https://brainly.com/question/23907081

#SPJ4

a) Sample means of sample 1 and sample 2 are 9 and 7 respectively.

b) Standard deviations of sample 1 and sample 2 are 2.28 and 2.82 respectively.

c) The 2 is a point estimate of the difference between the two population means.

d) The (- 0.687, 4.687) is 90% confidence interval estimate of the difference between the two population means.

We have data of two samples say sample 1 and sample 2. A sample mean is an average of a set of data that is measure of the center of the data. It is equal to the addition of data values divided by the total number of values. Mathematically, \(\bar x=\frac{{\sum_{i=1}^{n}X_i}}{n}\)

where Xᵢ --> data values

n --> total number of data values

Now, let \(\bar x_1\) and \(\bar x_2\) be sample means of sample 1 and sample 2. \(\bar x_1 = \frac{{\sum X_i}_{i=1}^{n} X_i}{n}\)

\(= \frac {10 + 7 + 13 + 7 + 9+ 8 }{6} = 9\)

\(\bar x_2 = \frac{{\sum X_i}_{i=1}^{n} X_i}{n}\)

\(= \frac {8 + 7 + 8 + 4 + 6+ 9}{6}= 7\)

So, required value are 9 and 7.

b) Formula for standard deviations is

\(s² = \sqrt { \frac{ \sum_{i = 1}^{n} (X_i - \bar x )^2 }{n - 1}}\)

Let s₁ and s₂ be standard deviations for sample 1 and 2 respectively. So, \(s_1^{2} = \sqrt { \frac{ \sum_{i = 1}^ {n} (X_i - \bar x )^2 }{n - 1}}\)

\( = \sqrt {\frac{(10 - 9)²+ (7 - 9)²+ (13 - 9)²+ (7- 9)² + (9 - 9)²+ (8 - 9)²}{6 - 1}} \\ \)

= 2.280

\(s_2^{2} = \sqrt { \frac{ \sum_{i = 1}^ {n} (X_i - \bar x )^2 }{n - 1}}\)

\( = \sqrt { \frac{( 8 - 7)² + ( 7 - 7)²+ (8 - 7)² + (4- 7)² + (6- 7)² + (9- 7)² }{6 - 1}} \\ \)

= 2.820

c) The point estimate of the means difference, \(\hat d = \bar x_1 - \bar x_2\)

= 9 - 7 = 2

d) Now, the pooled standard deviations,

\( {s_p}^2 = \frac{( n_1 - 1) s_1^2 + (n_2 - 1)s_2^2}{ n_1 + n_2 - 1}\)

\(=\frac{5(2.28)²+ 5( 2.82)²}{6 + 6 -1}\) = 6.5980

Degree of freedom = 5 + 5 - 1 = 9

Using distribution table, the z -score for 90% confidence interval and degree of freedom, 9 is 1.812. So, the confidence interval, \(CI = (\bar x_1 - \bar x_2) ± z^{*}\sqrt {\frac{s_1^2 }{n_1} + \frac{s_2^2 }{n_2}}\)

\(= ( 9 - 7) ± \sqrt { \frac{2.28²}{6} + \frac{2.82²}{6}}\)

= 2 ± 1.812× 1.480

= (- 0.687, 4.687)

Hence, required interval value is (- 0.687, 4.687).

For more information about confidence interval, visit:

https://brainly.com/question/17212516

#SPJ4

Complete question:

Consider the above data for two independent random samples taken from two normal populations.

a. Compute the two sample means. (to nearest whole number)

b. Compute the two sample standard deviations. (to 2 decimals)

c. What is the point estimate of the difference between the two population means?

d. What is the 90% confidence interval estimate of the difference between the two population means?(to 2 decimals and enter negative value as negative)

Answer:

3CuCl2 + 2Ni → 3Cu + 2NiCl3

Answer:

the first one

Step-by-step explanation:

Answer:

148 books

Step-by-step explanation:

Answer:

148 books all together

A line, line segment, or ray that divides an angle into two congruent angles is called an angle bisector.

What are supplementary angles example?

Supplementary angles are those angles that sum up to 180 degrees. For example, angle 130° and angle 50° are supplementary angles because sum of 130° and 50° is equal to 180°. Similarly, complementary angles add up to 90 degrees.

What do you mean by angle bisector?

If the angle is divided by the line and the angle is divided such that the angles are equal to each other then the line is called the angle bisector.

The word congruent means equal of the things. In this, the angles are congruent to each other which means the angles are equal to each other.

Thus, the black space is to be filled by the angle bisector.

More about the angle bisector line is given below.

brainly.com/question/3642603

#SPJ4

Answer:

\(in standard notation \: 9 { \times 10}^{ - 4} = 0.0009\)

The Fahrenheit temperature of the cup of water, after 4.5 minutes, is given as follows:

155ºF.

The temperature function is defined as follows:

\(T(t) = T_a + (T_0 - T_a)e^{-kt}\)

Considering the surrounding and initial temperature, we have that the function is given as follows:

\(T(t) = 69 + 135e^{-kt}\)

The temperature after 1.5 minutes is of 185ºF, hence the coefficient k is obtained as follows:

\(185 = 69 + 135e^{-1.5k}\)

\(e^{-1.5k} = \frac{116}{135}\)

\(k = -\frac{\ln{\left(\frac{116}{135}\right)}}{1.5}\)

k = 0.1011.

Hence:

\(T(t) = 69 + 135e^{-0.1011t}\)

Hence the temperature after 4.5 minutes is given as follows:

\(T(4.5) = 69 + 135e^{-0.1011 \times 4.5}\)

T(4.5) = 155ºF.

More can be learned about Newton's Law of Cooling at https://brainly.com/question/10321943

#SPJ1

Answer:

thats 5:40 am in normal time

Step-by-step explanation:

the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

Here we have the quadratic equation:

f(x) = (x + 3)*(x + 5)

The first claim is: "The y-intercept is at (15, 0)."

This is clearly false, as the y-intercept is at x = 0, and in that point we have x = 15.

The second claim is:

"The x-intercepts are at (–3, 0) and (5, 0)"

This is false, in the factored equation we can see that the x-intercepts are x =-3 and x = -5.

Third claim:

"The vertex is at (-4, -1)"

The middle value between the zeros is:

(-3 + (-5))/2 = -4

Evaluating the function in x = -4 we get the y-value of the vertex:

f(-4) = (-4 + 3)*(-4 + 5) = -1*1 = -1

So the vertex is at (-4, -1), this claim is true.

The fourth claim is:

"The midpoint between the x-intercepts is at (4, 0)."

Which is false, we already saw that the midpoint between the x-intercepts is at x = -4

Then the only student that is correct is Stepheh. "The vertex is at (–4, –1)."

If you want to learn more about quadratic equations:

https://brainly.com/question/1214333

#SPJ1

Answer:

n = 27

Step-by-step explanation:

multiply each term by 3 and simplify.

The solution of the equation is N = 27 .

Given,

N/3 = 9

Now,

To get the value of N ,

Rewriting the equation in form,

N/3 = 9/1

Now apply cross multiplication,

N * 1 = 9 * 3

N = 27

Thus the solution of the equation is 27 .

Know more about equations,

https://brainly.com/question/379059

#SPJ6

Answer:

-132

Step-by-step explanation:

24-24)-(144-12)

0-132

-132

The equation y = 3/4x describes the relationship

From the question, we have the following parameters that can be used in our computation:

The graph

The graph is a linear graph, and we have the following points on the graph

(x, y) = (0, 0) and (4, 3)

Because the line passes through the origin i.e. (0, 0), the equation that describes the relationship is then represented as

y = Y/X * x

Where

(X, Y) = (4, 3)

So, we have

y = 3/4x

Hence, the equation is y = 3/4x

Read more about linear equations at

https://brainly.com/question/4074386

#SPJ1

Answer:

16x+6

Step-by-step explanation:

5x+2+3x+1+5x+2+3x+1 =

16x+6

Answer:

16x + 2

Step-by-step explanation:

\(\boxed{\begin{minipage}{4 cm}\underline{Perimeter of a rectangle}\\\\$P=2(w+l)$\\\\where:\\ \phantom{ww}$\bullet$ $w$ is the width. \\\phantom{ww}$\bullet$ $l$ is the length.\\\end{minipage}}\)

Given expressions:

To write an expression for the perimeter of the rectangle, substitute the given expressions for the width and length into the perimeter formula:

\(\begin{aligned}\implies \textsf{Perimeter} &=2\left(5x+2+3x-1 \right)\\ &= 2(5x+3x+2-1)\\&=2(8x+1)\\&=16x+2\end{aligned}\)

Answer:

7²-4²

49-16= 33

33/3= 11

Therefore 33 is a multiple of 3 because 3×11= 33 and 3 can be divided by 33 without leaving a remainder

Answer:

a) What distance did he cover?

9 km

b) What was his displacement?

6.71kmSE

Step-by-step explanation:

a) What distance did he cover?

Total distance covered = 6km south + 3km east = 9km

b) What was his displacement?

Displacement =√( 6km)² + (3km)²

=√ 36 + 9

= √45

= 6.7082039325kmSE(SouthEast)

Approximately = 6.71kmSE

Answer:

Step-by-step explanation:

-7y=42

we have to divide by 7

-y=6

multiply by -1

y=-6

Answer:

y=-6

Step-by-step explanation:

divide by -7 on both sides.

Answer:

A' (3, 8 )

Step-by-step explanation:

Applying the translation rule to A (1, 3 )

A (1, 3 ) → A' (1 + 2, 3 + 5 ) → A' (3, 8 )

In an exponential expression, a base is a number that is raised to a certain power, represented by the exponent. The base can be any real number, while the exponent must be a positive integer.

Some key points to remember about the base and exponent in an exponential expression are:

For example, in the expression "2^3" (read as "2 raised to the power of 3"), the base is 2 and the exponent is 3. This means that 2 is being multiplied by itself 3 times (222 = 8). So the expression evaluates to 8.

Learn more about exponents here:

https://brainly.com/question/13669161

#SPJ4

The solutions to the equation \(15z^2 +6z -8 =4z\) are z = 2/3 or z = -4/5.

To solve the quadratic equation \(15z^2 +6z -8 =4z\), we first need to rearrange it into standard form:

\(15z^2 + 2z - 8 = 0\)

Now we can apply the quadratic formula:

z = (-b ± √(b² - 4ac)) / 2a

where a = 15, b = 2, and c = -8.

Plugging in these values, we get:

z = (-2 ± √(2² - 4(15)(-8))) / (2(15))

z = (-2 ± √(4 + 480)) / 30

z = (-2 ± √484) / 30

z = (-2 ± 22) / 30

So z equals either (-2 + 22)/30 = 2/3 or (-2 - 22)/30 = -4/5.

Therefore, the solutions to the equation 15z² +6z -8 =4z are z = 2/3 or z = -4/5.

To know more about the quadratic equations

https://brainly.com/question/28038123

#SPJ1

Answer:

\((2x+7)(x+3)\)

Step-by-step explanation:

\(2x^2+13x+21\)

To solve, we will need to factor.

\(2x^2+13x+21\)

Now we got an answer!

\((2x+7)(x+3)\)

This is your answer!

Hope this helps!

Answer:

c. -2a - 12

Step-by-step explanation:

use distributive property

Answer:

C f

Step-by-step explanation:

-2(a+6) just distrubit the -2 which you will get -2a-12

n the case of errors-in-variables bias, the OLS estimator is consistent but no longer unbiased in small samples. This is the correct statement.

In statistics, the errors-in-variables bias is a form of statistical bias that occurs when an independent variable (IV) is measured with error. The presence of the errors-in-variables (EIV) bias means that the OLS estimator will be consistent but no longer unbiased. This means that the OLS estimator can still give reliable estimates, but the estimates are no longer accurate.

The errors-in-variables (EIV) bias can be corrected by using methods such as instrumental variables or two-stage least squares (2SLS) regression. In small samples, the EIV bias can have a more significant impact on the accuracy of the OLS estimator.

In such cases, other estimation methods such as maximum likelihood estimation or the generalized method of moments (GMM) may be used to improve the accuracy of the estimates

Therefore, option C: the OLS estimator is consistent but no longer unbiased in small samples, is the correct .

Know more about the least squares (2SLS) regression

https://brainly.com/question/14563186

#SPJ11

Hi

exponnential cannot be negative.  So A is out  

quadratic function cannot also. So B is out.  

C is the only one remaining...

Answer: the new one is A. Sorry i mistaked C but ik A is right. I re-did the problem

I hope i helped and can i be marked brainliest if i got it right?

if i did not get it right, therefore please forgive me please.

Answer:

2

Step-by-step explanation:

Answer:

please it is B

give thanks if it helps

If x + 3/4 = 1 then the point on the number line shown figure is B.

We have given that,

if x + 3/4 = 1 then which point on the number line shown below could be x.

A number line is a picture of a graduated straight line that serves as abstraction for real numbers, denoted by R. Every point of a number line is assumed to correspond to a real number and every real number to a point.

Therefore, if x + 3/4 = 1 then the point on the number line shown figure is B.

To learn more about number lines visit:

https://brainly.com/question/25230781

#SPJ2

3,708,000,000 in  scientific notation is \(3.708\) × \(10^9\)